RecursiveFactorization.jl VS blis

What about the other benchmarks on the same site? https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Bio/BCR/ BCR takes about a hundred seconds and is pretty indicative of systems biological models, coming from 1122 ODEs with 24388 terms that describe a stiff chemical reaction network modeling the BCR signaling network from Barua et al. Or the discrete diffusion models https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Jumps/Dif... which are the justification behind the claims in https://www.biorxiv.org/content/10.1101/2022.07.30.502135v1 that the O(1) scaling methods scale better than O(log n) scaling for large enough models? I mean.

> If you use special routines (BLAS/LAPACK, ...), use them everywhere as the respective community does.

It tests with and with BLAS/LAPACK (which isn't always helpful, which of course you'd see from the benchmarks if you read them). One of the key differences of course though is that there are some pure Julia tools like https://github.com/JuliaLinearAlgebra/RecursiveFactorization... which outperform the respective OpenBLAS/MKL equivalent in many scenarios, and that's one noted factor for the performance boost (and is not trivial to wrap into the interface of the other solvers, so it's not done). There are other benchmarks showing that it's not apples to apples and is instead conservative in many cases, for example https://github.com/SciML/SciPyDiffEq.jl#measuring-overhead showing the SciPyDiffEq handling with the Julia JIT optimizations gives a lower overhead than direct SciPy+Numba, so we use the lower overhead numbers in https://docs.sciml.ai/SciMLBenchmarksOutput/stable/MultiLang....

> you must compile/write whole programs in each of the respective languages to enable full compiler/interpreter optimizations

You do realize that a .so has lower overhead to call from a JIT compiled language than from a static compiled language like C because you can optimize away some of the bindings at the runtime right? https://github.com/dyu/ffi-overhead is a measurement of that, and you see LuaJIT and Julia as faster than C and Fortran here. This shouldn't be surprising because it's pretty clear how that works?

I mean yes, someone can always ask for more benchmarks, but now we have a site that's auto updating tons and tons of ODE benchmarks with ODE systems ranging from size 2 to the thousands, with as many things as we can wrap in as many scenarios as we can wrap. And we don't even "win" all of our benchmarks because unlike for you, these benchmarks aren't for winning but for tracking development (somehow for Hacker News folks they ignore the utility part and go straight to language wars...).

If you have a concrete change you think can improve the benchmarks, then please share it at https://github.com/SciML/SciMLBenchmarks.jl. We'll be happy to make and maintain another.

Ask them to download Julia and try it, and file an issue if it is not fast enough. We try to have the latest available.

See for example: https://github.com/JuliaLinearAlgebra/RecursiveFactorization...

Julia defaults to OpenBLAS but libblastrampoline makes it so that `using MKL` flips it to MKL on the fly. See the JuliaCon video for more details on that (https://www.youtube.com/watch?v=t6hptekOR7s). The recursive comparison is against OpenBLAS/LAPACK and MKL, see this PR for some (older) details: https://github.com/YingboMa/RecursiveFactorization.jl/pull/2... . What it really comes down to in the end is that OpenBLAS is rather bad, and MKL is optimized for Intel CPUs but not for AMD CPUs, so when the best CPUs are now all AMD CPUs, having a new set of BLAS tools and mixing that with recursive LAPACK tools is either as good or better on most modern systems. Then we see this in practice even when we build BLAS into Sundials for 1,000 ODE chemical reaction networks (https://benchmarks.sciml.ai/html/Bio/BCR.html).

>I hope those benchmarks are coming in hot

M1 is extremely good for PDEs because of its large cache lines.

https://github.com/SciML/DiffEqOperators.jl/issues/407#issue...

The JuliaSIMD tools which are internally used for BLAS instead of OpenBLAS and MKL (because they tend to outperform standard BLAS's for the operations we use https://github.com/YingboMa/RecursiveFactorization.jl/pull/2...) also generate good code for M1, so that was giving us some powerful use cases right off the bat even before the heroics allowed C/Fortran compilers to fully work on M1.

Not necessarily true with Julia. Many libraries like DifferentialEquations.jl are Julia all of the way down because the pure Julia BLAS tools outperform OpenBLAS and MKL in certain areas. For example see:

https://github.com/YingboMa/RecursiveFactorization.jl/pull/2...

So a stiff ODE solve is pure Julia, LU-factorizations and all.

Also, the major point is that BLAS has little to no role played here. Algorithms which just hit BLAS are very suboptimal already. There's a tearing step which reduces the problem to many subproblems which is then more optimally handled by pure Julia numerical linear algebra libraries which greatly outperform OpenBLAS in the regime they are in:

https://github.com/YingboMa/RecursiveFactorization.jl#perfor...

And there are hooks in the differential equation solvers to not use OpenBLAS in many cases for this reason:

https://github.com/SciML/DiffEqBase.jl/blob/master/src/linea...

Instead what this comes out to is more of a deconstructed KLU, except instead of parsing to a single sparse linear solve you can do semi-independent nonlinear solves which are then spawning parallel jobs of small semi-dense linear solves which are handled by these pure Julia linear algebra libraries.

And that's only a small fraction of the details. But at the end of the day, if someone is thinking "BLAS", they are already about an order of magnitude behind on speed. The algorithms to do this effectively are much more complex than that.

BLIS is an interesting new direction in that regard: https://github.com/flame/blis

>The BLAS-like Library Instantiation Software (BLIS) framework is a new infrastructure for rapidly instantiating Basic Linear Algebra Subprograms (BLAS) functionality. Its fundamental innovation is that virtually all computation within level-2 (matrix-vector) and level-3 (matrix-matrix) BLAS operations can be expressed and optimized in terms of very simple kernels.

There is a recent update to the blis alternative to BLAS that includes a number of RISC-V performance optimizations.

https://github.com/flame/blis/pull/737

https://github.com/flame/blis/blob/master/docs/Performance.m...

It seems that the selling point is that BLIS does multi-core quite well. I am especially impressed that it does as well as the highly optimized Intel's MKL on Intel's CPUs.

I do not see the selling point of BLIS-specific APIs, though. The whole point of having an open BLAS API standard is that numerical libraries should be drop-in replaceable, so when a new library (such as BLIS here) comes along, one could just re-link the library and reap the performance gain immediately.

What is interesting is that numerical algebra work, by nature, is mostly embarrassingly parallel, so it should not be too difficult to write multi-core implementations. And yet, BLIS here performs so much better than some other industry-leading implementations on multi-core configurations. So the question is not why BLIS does so well; the question is why some other implementations do so poorly.

First we can use Laser, which was my initial BLAS experiment in 2019. At the time in particular, OpenBLAS didn't properly use the AVX512 VPUs. (See thread in BLIS https://github.com/flame/blis/issues/352 ), It has made progress since then, still, on my current laptop perf is in the same range

Reproduction:

https://github.com/flame/blis/

Field et al, recent winners of the James H. Wilkinson Prize for Numerical Software.

Field and Goto both worked with Robert van de Geijn. Lots of TACC interaction in that broader team.

BLIS is fine too~ https://github.com/flame/blis

Here's BLIS's object API:

https://github.com/flame/blis/blob/master/docs/BLISObjectAPI...

Searching "object" in BLIS's README (https://github.com/flame/blis) to see what they think of it:

"Objects are relatively lightweight structs and passed by address, which helps tame function calling overhead."

"This is API abstracts away properties of vectors and matrices within obj_t structs that can be queried with accessor functions. Many developers and experts prefer this API over the typed API."

In my opinion, this API is a strict improvement over BLAS. I do not think there is any reason to prefer the old BLAS-style API over an improvement like this.

Regarding your own experience, it's great that using BLAS proved to be a valuable learning experience for you. But your argument that the BLAS API is somehow uniquely helpful in terms of learning how to program numerical algorithms efficiently, or that it will help you avoid performance problems, is not true. It is possible to replace the BLAS API with a more modern and intuitive API with the same benefits. To be clear, the benefits here are direct memory management and control of striding and matrix layout, which create opportunities for optimization. There is nothing unique about BLAS in this regard---it's possible to learn these lessons using any of the other listed options if you're paying attention and being systematic.

The article asks "Which Micro-optimizations matter for BLAS3?", implying small dimensions, but doesn't actually tell me. The problem is well-studied, depending on what you consider "small". The most important thing is to avoid the packing step below an appropriate threshold. Implementations include libxsmm, blasfeo, and the "sup" version in blis (with papers on libxsmm and blasfeo). Eigen might also be relevant.

https://libxsmm.readthedocs.io/

https://blasfeo.syscop.de/

https://github.com/flame/blis